Project Management

Management

• Management• in all business and organizational activities

is the act of getting people together to accomplish desired goals and objectives using available resources efficiently and effectively.

• 1- The science and art of getting things done through others.2- Is the action of getting people together to complete objectives and goals using available reasons effectively

• is the process of getting activities completed efficiently and effectively with and through other people.

• Management is decision making

purposes they serve. These processes are aggregated into five groups, defined as theProject Management function Process

• • Initiating Process• • Planning Process• Organizing Process• • Executing Process• • Monitoring and Controlling Process• • Closing Process

planning• t is the basic function of management. It deals with chalking out a

future course of action & deciding in advance the most appropriate course of actions for achievement of pre-determined goals. According to KOONTZ, “Planning is deciding in advance - what to do, when to do & how to do. It bridges the gap from where we are & where we want to be”. A plan is a future course of actions. It is an exercise in problem solving & decision making. Planning is determination of courses of action to achieve desired goals. Thus, planning is a systematic thinking about ways & means for accomplishment of pre-determined goals. Planning is necessary to ensure proper utilization of human & non-human resources. It is all pervasive, it is an intellectual activity and it also helps in avoiding confusion, uncertainties, risks, wastages etc.

is the management of the organization's future in an uncertain environment.1. Revising project goals and objective.

•2. Creating the project management plane.•3. Determining the alternative.

•4. Forecasting the future.

organizing• t is the process of bringing together physical, financial and human

resources and developing productive relationship amongst them for achievement of organizational goals. According to Henry Fayol, “To organize a business is to provide it with everything useful or its functioning i.e. raw material, tools, capital and personnel’s”. To organize a business involves determining & providing human and non-human resources to the organizational structure. Organizing as a process involves:

• Identification of activities.• Classification of grouping of activities.• Assignment of duties.• Delegation of authority and creation of responsibility.• Coordinating authority and responsibility relationships.

• Division of LabourDepartmentalizationSpecialization

• Unity of CommandLine of commandOne superior

• Authority and ResponsibilityLine and staff authority Authority and power• Spans of Control• Levels of control

Centralization and decentralization

Implementation • Put plan into action• We have a detailed work plan• Now, we get the work underway• We do this by:

– Choosing participants– Making participants available for the project– Assigning work to participants– Organizing participants into team(s)– Providing resources to the team(s)– Establish constraints and freedoms for the team(s)

controlling• It implies measurement of accomplishment against the standards and

correction of deviation if any to ensure achievement of organizational goals. The purpose of controlling is to ensure that everything occurs in conformities with the standards. An efficient system of control helps to predict deviations before they actually occur. According to Theo Haimann, “Controlling is the process of checking whether or not proper progress is being made towards the objectives and goals and acting if necessary, to correct any deviation”. According to Koontz & O’Donell “Controlling is the measurement & correction of performance activities of subordinates in order to make sure that the enterprise objectives and plans desired to obtain them as being accomplished”. Therefore controlling has following steps:

• Establishment of standard performance.• Measurement of actual performance.• Comparison of actual performance with the standards and finding out

deviation if any.• Corrective action.

Project Management Emergence

• Explosion in human knowledge

• Mass customization of products and services

• Expansion of global markets

Forces Of Project Management

• Forces driving Project Management:– 1. exponential expansion of human knowledge– 2. growing demand for a broad range of complex,

sophisticated, customized goods and services– 3. evolution of worldwide competitive markets for the

production and consumption of goods and services

• Team-based problem solving v. individual

The Professionalism of Project Management

• Complexity of problems facing the project manager• Growth in number of project oriented organizations

– The Project Management Institute (PMI) was established in 1969

– By 1990 it had 7,500 members– 1995, over 17,000 members– 1998--exploded to over 44,000 members

• This exponential growth is indicative of the rapid growth in the use of projects

• Importance of PMI as a force in the development of project management as a profession

The Definition of a “Project”

• Must make a distinction between terms:– Program - an exceptionally large, long-range

objective that is broken down into a set of projects– Task - set of activities comprising a project– Work Packages - division of tasks– Work Units - division of work packages

• A specific, finite task to be accomplished

Project Management A Working Definition

• Project:– A problem with a known solution scheduled for

completion—unique and non-routine activities– A project is a sequence of unique complex and

connected activities and having one goal or purpose and that must be completed by a specific time within budget and according to specifications.

A project is a temporary endeavor undertaken to create a unique product, service, or result.Temporary

•has a definite beginning and a definite end, not ongoing efforts.•Ceases when objectives have been attained.•Team disbanded upon completion.

What is the project

What is the project (continue)

Unique:the product or services is different in some way from other products or services.The presence of repetitive element does not change the fundamental uniqueness of the project work.

Progressively Elaborated:Progressively means “proceeding in steps” containing steadily by increments.Elaborated means “worked out with care and detail; developed thoroughly”.

PROJECT IS CONVERTING

•IDEA CONCRETE INTETY

DESIGN FACTORYPLAN BUILDING

HIGHWAYSERVICES

• PRODUCTS•

• PROJECTS PRODUCTIONS• AUTOMOBILE FACTORY PRDUCE AUTOMOBILE• BUILD A HOUSE OPERATE HOUSEHOLDE• CONSTRUCT HOSPITAL TREAT PATIENTS• CONCEIVE NEW PRODUCT MANUFACTURE• DONE ONCE DONE REPETITIVELY

NATURE OF PROJECT AND PRODUCTION

input Altering (add value) OutputTRANSFORMATION

desirable & undesirable• Men• Machine Environment• Money Economic• Materials Social• Management Political

Feed Back

Projects versus operations

Similarities between project and operations• Both performed by people even 1 person.• Both are constrained by recourses.• Both are planned, executed and controlled.• Both are done for a purpose and have interrelated activities.

Difference between projects and operations• Operations are on going and repetitive.• Projects are temporary endeavor undertaken to create unique

products or services that are progressively elaborated.

• Projects are typically authorized as a result of one or more of the following strategic considerations:

• A market demand.• An organizational need.• A customer request.• A technological advanced.• A legal requirement.

Projects and strategic

• The application of knowledge, skills, tools, and techniques to project activities in order to meet stakeholder needs and expectations.

• Managing a project includes:• Identifying requirement • Establishing Clear and achievable objectives• Balancing the competing demands for quality, scope, time and cost.• Adapting the specifications ,plans, and approach to the different concerns and expectations of the various stakeholders

What is Project Management?

What is project management?

• Project Management:– The science and art of solving the problem

within predetermined time and resource parameters

– Project management is the application of skills knowledge tools and techniques to meet the needs and expectations of stakeholders for a project.

– Shouldering just enough risk to escape with your career intact!!!

What is Project Management?

• Project managers:Often talk of a “triple constraint”- project scope, time and

cost in managing competing project requirements. Project quality is affected by balancing these three factors.

• The project management team:has a professional responsibility to there stakeholders including

customers,the performing organization, and the public.

Triple Constraint

Quality

Scope

Time

Cost

• Project management is a set of principles and tools for :• -Defining• -planning• -executing• -controlling• -completing a project• Projects are oriented towards a goal• There is something unique about every project• Projects have a finite duration• Project require coordination of interrelated activities

Project objectives:

• Construction projects are often complex with potential for cost and time

• Overruns or the finished facility performing less well than planned to minimize risks the client should select the contract strategy that matches the objectives of the project. These must be clearly established and prioritized before any design or other work begins.

• The client must decide the relative importance of the three main objectives time, cost and performance of the completed project

Objectives of a Project• Project Objectives:

– Performance– Time– Cost

• Expectations of clients inherent part of the project specifications

Objectives of a Project• 3 Project Objectives:

Characteristics of a Project

• 1- Uniqueness: one time operational non repetitive .• 2- limited time and resource .• 3- establish to achieve specific objectives .• 4- well defined collection of activities.• 5-Interdependencies

Why Project Management?• Companies have experienced:

– Better customer relations– Shorter overall delivery times– Lower costs and higher profit margins– Higher quality and reliability– Higher worker morale

Why (not) Project Management?• Companies have also experienced some

negatives:– Greater organizational complexity– Increased likelihood of organizational policy

violations– Higher costs– More management difficulties– Low personnel utilization

The Project Life Cycle

• Stages of a Conventional Project:– Slow beginning– Buildup of size– Peak– Begin a decline– Termination

The Project Life Cycle

• Selection of the project• Project planning

scope of work & network developmentbasic schedulingtime cost tradeoffsresource considerations in projects

Project Implementation Project controlling and completion

Selection of the project

• Project identification• Project appraisal• Project selection

Project identification

• Receptive to new ideas• Vision of future growth• Long term objectives• SWOT analysis• Preliminary project analysis

Project appraisal

• Market appraisal• Technical appraisal• Financial appraisal• Economics appraisal• Ecological appraisal• A feasibility report considers all these issues prior

to project adoption

Market appraisal

.Aggregate future demand

• Market share• Current and future competition• Location and accessibility of consumers• Technological scenario /obsolescence• Possible pricing option

Technical appraisal

• Engineering aspects• Location• Size• Production process

Financial appraisal

• Cash flow over time• Profitability• Break event point• Net present value• Internal rate of return• Payback period• Risk

Economic appraisal

•• Benefits and costs(in shadow prices)• Distribution of income in society• Level of savings and investment in society• Self sufficiency ,employment and social

order

Ecological appraisal

• Environmental damage• Air• Water• Noise• Other• Restoration measures and cost

Basic scheduling

• Project representation as network• Estimation of activity durations• Forward and backward passes• Determination of activity floats• Critical path for selective control and

minimum project duration

Time cost tradeoff

• Normal and crash activity durations• Linear /nonlinear/discontinuous/discrete

time cost relationships• Project cost- duration efficient frontier• Total project (direct and indirect) Cost

Resource aggregation

• Project schedule• Resource consumption profile for each resource• Provisioning of resource over time• Project Scheduling and Control Techniques• Gantt Chart• Critical Path Method (CPM)• Program Evaluation and Review Technique

(PERT)

The Project Life Cycle

• Projects also exist which do not follow the conventional project life cycle

• Comprised of subunits that have little use as a stand alone unit, yet become useful when put together

The Project Life Cycle

• Time distribution of project effort is characterized by slow-rapid-slow

Project Management Life CycleDefinition Planning Implementation Delivery

Lev

el o

f eff

ort

1. Goals2. Specifications3. Scope4. Responsibilities5. Teams

1. WBS2. Budgets3. Resources4. Risks5. Schedule

1. Status reports2. Change Orders3. Quality Audits4. Contingencies

1. Train user2. Transfer documents3. Release resources4. Reassign staff5. Lessons learned

Proactive Project Life Cycle

Levelof ValueofEffort

Low

High

Define Plan Implement DeliveryScope WBS/OBS/Schedule Resource (Re)allocation “Learn Curve”

Tradeoffs Detailed Budget Cost Containment Final Report

Project Evaluation (Audit) Process

Change Management System

Project Manager Roles and Responsibilities

Closed-Loop Planning-Monitor-Control System

• PMI talks about five types of organizational structure, based upon project manager’s level of authority.

• Organizational structure can be characterized as scanning a spectrum from functional to projectized

as follows: Functional Organization .Weak, balanced and strong Matrix Organization. Project zed Organization.

Forms of Organization

Functional Organization

This is the most common form oforganization. The organization is grouped by areas of specializationwithin differentfunctional areas(e.g. accounting, Marketing and manufacturing).

• Easier Management of specialists.• Team reporting to 1 supervisor.• Similar resources are centralized and grouped by

specialty.• Clear career path in areas of specialty.• Job security is guaranteed.• More focus on the specialty than over the concern for

the project success.• No career path in PM.• PM has no authority.

Advantages of Functional Organizations

All organization is run by projects. The Project Manager has total control of projectsPersonnel are assigned and report to a Project Manager.

Project zed Organization

• Advantages:1. Project Manager has the power and full

authority over the project’s resources.2. Communication are easier and faster.

• Disadvantages:1. No career path in areas of specialty.2. No job security.

Advantages & disadvantages of Project zed Organizations

• This form is an attempt to maximize the strengths and weaknesses of both the functional and project forms.

• In a strong matrix, power rests with the project Manager. In a weak matrix, power rests with the functional manager.

• In a balanced matrix, the power is shared between the functional manager and the Project Manager.

Matrix Organization

Weak matrix Organization

In this from oforganization, theproject expeditoracts primarily as astaff assistant and communicationscoordinator. The expeditor cannotpersonally make orenforce decisions

This form of organization is similar to the Weak Matrix organization,except that thecoordinator has some power to make decisions,some authority and reports to higher-level manager.

Balanced Matrix

Strong Matrix

• Advantages: Both Project Manager and functional managers share the responsibility of the project’s resources.

• Disadvantages: There is more than one boss for the project team. Communications are complex as the team members should make dual reporting.

Advantages & disadvantagesof matrix Organizations

Organization Structure versusProject Characteristics

Project planning

• Defining scope and terms of reference• Work break down structure• Basic scheduling • Time cost tradeoffs• Resources considerations

Project Planning

• Resource Availability and/or Limits– Due date, late penalties, early completion

incentives– Budget

• Activity Information– Identify all required activities– Estimate the resources required (time) to complete

each activity– Immediate predecessor(s) to each activity needed

to create interrelationships

Work breakdown structure• A method of breaking down a project into individual

elements ( components, subcomponents, activities and tasks) in a hierarchical structure which can be scheduled and cost

• It defines tasks that can be completed independently of other tasks, facilitating resource allocation, assignment of responsibilities and measurement and control of the project

• It is foundation of project planning• It is developed before identification of dependencies and

estimation of activity durations• It can be used to identity the tasks in the CPM and PERT

Ways that WBS based on :

• Hard work orientation identification of basic work package

• Agency organization : Based on assignment of responsibility to different agencies (some subcontractors, agencies)

• Function oriented (e.g. design , Procurement , construction).

• WBS doesn’t show sequence of work and breakdown a project only to levels sufficient to produce an estimate required accuracy (+ or – )10 % .

work breakdown structure

• 1-generally WBS includes 6-7 levels. more or less may be needed for a situation

• 2-all paths on a WBS do not go down to the same levels

• 3-WBS does not show the sequencing of work.• 4-WBS should be developed before scheduling

and resource allocation are done.

Work Breakdown Structure for Computer Order Processing System Project

Work breakdown structure

• Work breakdown structure should be developed by individuals knowledgeable about the work .

• This means that levels will be developed by various groups of and the separate parts combined . Outputs of WBS :-

• Detailed list of activity.• Easy to estimate cost and resource • Easy to estimate duration.

Project representation

• 1-project name and description .• 2- list of activities that constitute the project .• 3-Gantt or bar chart showing when activities take

place .• 4-project network showing activities, there

dependencies and there relation to the whole activities.(AOA and AON)Representations.

Project Scheduling and Control Techniques

Gantt Chart

Critical Path Method (CPM)Program Evaluation and Review Technique (PERT)

• Gantt bar chart : an old to prepare this chart we need to

• Carefully examine the scope of the project and then adopt a strategy for the performance (divide the project to units)

• Divide the project into units then to activities(by WBS :work break-down structure).the activity was divide into sub activities.

• Estimate time required to finishing these activities (duration) time

• Assign a priority of dependency for each activity• Draw a bar chart according to the priority of dependency

Graph or bar chart with a bar for each project activity that shows passage of time

Provides visual display of project schedule

Gantt Chart

Gantt Charts• The Gantt chart shows planned and actual

progress for a number of tasks displayed against a horizontal time scale

• It is an effective and easy-to-read method of indicating the actual current status for each set of tasks compared to the planned progress for each item of the set

• It can be helpful in expediting, sequencing, and reallocating resources among tasks

• Gantt charts usually do not show technical dependencies

Disadvantages of Gantt bar chart :

• Doesn’t show critical activities(T.F =0)• Doesn’t show floats• Doesn’t show the relationship between

activities• Not good for large scale project ,you can’t

trace the effect of delays

Project Network • Why use project network?

• A convenient way to show activities and precedence in relation to the whole project.

• Basis of project planning:• Responsibility allocation • Definition of subcontracting unite • Roles of different players.• Basic scheduling and establishment of work time tables.• Critical path determination and selective management control• Alternatives of project representation:• 1- Activity on a node (AON)• 2- Activity on arc (AOA)

History of CPM/PERT• Critical Path Method (CPM)

– E I Du Pont de Nemours & Co. (1957) for construction of new chemical plant and maintenance shut-down

– Deterministic task times– Activity-on-node network construction– Repetitive nature of jobs

• Project Evaluation and Review Technique (PERT)– U S Navy (1958) for the POLARIS missile program– Multiple task time estimates (probabilistic nature)– Activity-on-arrow network construction– Non-repetitive jobs (R & D work)

Scheduling Terminology• Activity - A specific task or set of tasks that are

required by the project, use up resources, and take time to complete

• Event - The result of completing one or more activities. An identifiable end state occurring at a particular time. Events use no resources.

• Network - The combination of all activities and events define the project and the activity precedence relationships

Project Network• Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects• Use of nodes and arrows

Arrows An arrow leads from tail to head directionally– Indicate ACTIVITY, a time consuming effort that is required to perform a

part of the work.Nodes A node is represented by a circle

- Indicate EVENT, a point in time where one or more activities start and/or finish.

• Activity– A task or a certain amount of work required in the project– Requires time to complete– Represented by an arrow

• Dummy Activity– Indicates only precedence relationships– Does not require any time of effort

• Event– Signals the beginning or ending of an activity– Designates a point in time– Represented by a circle (node)

• Network– Shows the sequential relationships among activities using nodes

and arrows

Activity-on-node (AON)

nodes represent activities, and arrows show precedence relationships

Activity-on-arrow (AOA)

arrows represent activities and nodes are events for points in time

Project Network

Scheduling Terminology

• Path - The series of connected activities (or intermediate events) between any two events in a network

• Cr itical - Activities, events, or paths which, if delayed, will delay the completion of the project. A project’s critical path is understood to mean that sequence of critical activities that connect the project’s start event to its finish event

Scheduling Terminology• An activity can be in any of these conditions:

– It may have a successor(s) but no predecessor(s) -starts a network

– It may have a predecessor(s) but no successor(s) -ends a network

– It may have both predecessor(s) and successor(s) - in the middle of a network

• Interconnections from horizontal links in vertical WBS

AOA Network Building Blocks

8079Install software

EventActivity

AOA Project Network for House

32 0

13

1 111 2 4 6 7

3

5

Lay foundation

Design house and obtain financing

Order and receive materials

Dummy

Finish work

Select carpet

Select paint

Build house

AON Project Network for House

13

22

43

31 5

1

61

71Start

Design house and obtain financing

Order and receive materials Select paint

Select carpet

Lay foundations Build house

Finish work

Situations in network diagram

AB

C

A must finish before either B or C can start

A

B

C both A and B must finish before C can start

D

C

B

Aboth A and C must finish before either of B or D can start

A

C

B

D

DummyA must finish before B can start

both A and C must finish before D can start

Concurrent Activities

2 3

Lay foundation

Order material

(a) Incorrect precedence relationship

(b) Correct precedence relationship

3

42

DummyLay foundation

Order material

1

2 0

Drawing Networks• Activity-on-Arrow (AOA) networks use arrows to

represent activities while nodes stand for events• Activity-on-Node (AON) networks use nodes to

represent activities with arrows to show precedence relationships

• The choice between AOA and AON representation is largely a matter of personal preference

Drawing example

• Act. Depend on • A --• B a • C a• D b,c• E c• F c

AOA4

5

1 32AApplication

approvalD

Serviceavailability

check

CTrafficstudy

BConstruction

plans

Partial AOA Network

2

3

1 4A

X

C

B

E

(A)

2

3

1 4A

B

C

X

E

(B)

2 31

4

A

B

XC

E

(C)

Partial AOA Network

2 31

4

A

B

CX

E

(D) 5D

2 31

4

A

B

CX

E

(E)

5

D

F?

Full AOA Network

KOLL BUSINESS CENTERCounty Engineers Design Department

2 31

4

A5

B

C10

X

5

15 06 7 8

0Y

F10

G170

H35

E15

D5

ActivityDuration

Legend

Activity-on-Node Network Fundamentals

X

Y

Z

Y and Z are preceded by X

Y and Z can begin at thesame time, if you wish

(B)

A B C

A is preceded by nothingB is preceded by AC is preceded by B

(A)

J

K

L

M

J, K, & L can all begin atthe same time, if you wish(they need not occursimultaneously)

All (J, K, L) must becompleted before M canbegin

but

X Z

AAY

(C)

(D)

Z is preceded by X and Y

AA is preceded by X and Y

History of CPM/PERT• Critical Path Method (CPM)

– E I Du Pont de Nemours & Co. (1957) for construction of new chemical plant and maintenance shut-down

– Deterministic task times– Activity-on-node network construction– Repetitive nature of jobs

• Project Evaluation and Review Technique (PERT)– U S Navy (1958) for the POLARIS missile program– Multiple task time estimates (probabilistic nature)– Activity-on-arrow network construction– Non-repetitive jobs

Network example 1

Activity predecessors A ---B ---C ---D a,bE b,c

Network example 2

Activity predecessors A ---B ---C ---D a,bE a,cF a,b,c

Network example 3

Dummies for uniqueness of activity representationActivity predecessors A ---B aC aD aE b,d,c

The role of dummies in project networks

• 1 correct representation of precedence logic• 2uniqueness of activity representation • 3-creation of single source and sink• 1,2 and 3 is used in AOA network • 3 only used in AON network

Inconsistent network

• A closed loop in a project network is a logical inconsistent

Prerequisites for a valid project network

• Necessary requirement :the project network must not have any cycles or loops ,since these represent logical inconsistencies in representation

• Desirable features: the project network should have the minimum numbers of dummies and on redundancies since these unnecessarily clutter the network

CPM calculation

• Path– A connected sequence of activities leading from

the starting event to the ending event• Critical Path

– The longest path (time); determines the project duration

• Critical Activities– All of the activities that make up the critical path

Forward Pass• Earliest Start Time (ES)

– earliest time an activity can start – ES = maximum EF of immediate predecessors

• Earliest finish time (EF)– earliest time an activity can finish– earliest start time plus activity time

EF= ES + t

Latest Start Time (LS)Latest time an activity can start without delaying critical path time

LS= LF - tLatest finish time (LF)

latest time an activity can be completed without delaying critical path timeLS = minimum LS of immediate predecessors

Backward Pass

CPM analysis• Draw the CPM network• Analyze the paths through the network• Determine the float for each activity

– Compute the activity’s floatfloat = LS - ES = LF - EF

– Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project

• Find the critical path is that the sequence of activities and events where there is no “slack” i.e.. Zero slack– Longest path through a network

• Find the project duration is minimum project completion time

CPM Example: • CPM Network

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17 h, 9

i, 6

j, 12

CPM Example• ES and EF Times

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17 h, 9

i, 6

j, 12

0 6

0 8

0 5

CPM Example

• ES and EF Times

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17 h, 9

i, 6

j, 12

0 6

0 8

0 55 14

8 21

6 23

6 21

CPM Example

• ES and EF Times

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17 h, 9

i, 6

j, 12

0 6

0 8

0 55 14

8 21 21 33

6 23 21 30

23 29

6 21

Project’s EF = 33

CPM Example

• LS and LF Times

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17

h, 9

i, 6

j, 12

0 6

0 8

0 55 14

8 21 21 33

6 23

21 30

23 29

6 21

21 33

27 33

24 33

CPM Example

• LS and LF Times

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17

h, 9

i, 6

j, 12

0 6

0 8

0 55 14

8 21 21 33

6 23

21 30

23 29

6 21

4 10

0 8

7 12 12 21

21 33

27 33

8 21

10 27

24 33

18 24

CPM Example• Float

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17

h, 9

i, 6

j, 12

0 6

0 8

0 55 14

8 21 21 33

6 23

21 30

23 29

6 21

3 9

0 8

7 12 12 21

21 33

27 33

8 21

10 27

24 33

9 24

3 4

3

3

4

00

77

0

CPM Example• Critical Path

a, 6

f, 15

b, 8

c, 5e, 9

d, 13

g, 17 h, 9

i, 6

j, 12

PERT • PERT is based on the assumption that an activity’s duration

follows a probability distribution instead of being a single value• Three time estimates are required to compute the parameters of

an activity’s duration distribution:– pessimistic time (tp ) - the time the activity would take if

things did not go well– most likely time (tm ) - the consensus best estimate of the

activity’s duration– optimistic time (to ) - the time the activity would take if things

did go well

Mean (expected time): te =tp + 4 tm + to

6

Variance: Vt =σ 2 =tp - to

6

2

Methods of inconsistency checking

• Topological ordering of activities• Fulkerson’s numbering rules• Squaring adjacency matrix

Network exampleIllustration of network analysis of a minor redesign of a product and its associated packaging.

The key question is: How long will it take to complete this project ?

For clarity, this list is kept to a minimum by specifying only immediate relationships, that is relationships involving activities that "occur near to each other in time".

Questions to prepare activity network• Is this a Start Activity? • Is this a Finish Activity? • What Activity Precedes this? • What Activity Follows this? • What Activity is Concurrent with this?